Details

sample117.0ms

Algorithm

intervals

Results

25.0ms	182×	body	80	valid
23.0ms	33×	body	1280	valid
20.0ms	25×	body	2560	valid
10.0ms	77×	body	80	nan
9.0ms	17×	body	640	valid
5.0ms	12×	body	320	valid
4.0ms	4×	body	5120	valid
1.0ms	5×	body	160	valid

simplify72.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	49
4	49
3	46
2	33
1	19
0	10

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.2b	(- (* b_2 b_2) (* a c))
1.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 175

Calls

4 calls:

57.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
17.0ms	(- (* b_2 b_2) (* a c))
43.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
60.0ms	(- (* b_2 b_2) (* a c))
109.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
79.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.7s

Counts

187 → 187

Iterations

Iter	Nodes
3	4034
2	1423
1	576
0	248

prune2.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
1.2b	(- (* b_2 b_2) (* a c))
1.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-sqr-sqrt`
170×	`*-un-lft-identity`
165×	`times-frac`
118×	`add-cube-cbrt`
61×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
15×	`add-exp-log`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube` `associate-/r/`
7×	`neg-mul-1` `flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`rec-exp` `sub-neg` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `pow-flip` `inv-pow`

Counts

4 → 261

Calls

4 calls:

41.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
12.0ms	(- (* b_2 b_2) (* a c))
20.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
69.0ms	(- (* b_2 b_2) (* a c))
110.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
91.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

273 → 273

Iterations

Iter	Nodes
2	2075
1	834
0	355

prune2.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
1.2b	(- (* b_2 b_2) (* a c))
1.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-sqr-sqrt`
170×	`*-un-lft-identity`
165×	`times-frac`
118×	`add-cube-cbrt`
61×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
15×	`add-exp-log`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube` `associate-/r/`
7×	`neg-mul-1` `flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`rec-exp` `sub-neg` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `pow-flip` `inv-pow`

Counts

4 → 261

Calls

4 calls:

46.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
8.0ms	(- (* b_2 b_2) (* a c))
28.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series408.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
66.0ms	(- (* b_2 b_2) (* a c))
97.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
105.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

273 → 273

Iterations

Iter	Nodes
2	2075
1	834
0	355

prune2.8s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.4b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
1.2b	(- (* b_2 b_2) (* a c))
1.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

181×	`prod-diff`
146×	`add-sqr-sqrt`
139×	`*-un-lft-identity`
130×	`add-cube-cbrt`
95×	`sqrt-prod`
62×	`distribute-rgt-in` `distribute-lft-in`
59×	`distribute-rgt-neg-in`
57×	`distribute-lft-neg-in`
19×	`neg-mul-1`
13×	`associate-l` `add-exp-log`
11×	`times-frac` `fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `associate-r`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `sub-neg` `prod-exp` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sqrt-div` `div-exp` `associate-*r/` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `neg-log` `associate-l/` `-commutative` `div-inv`

Counts

4 → 296

Calls

4 calls:

88.0ms	(* (/ 1 a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
9.0ms	(- (* b_2 b_2) (* a c))
27.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series361.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* (/ 1 a) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
41.0ms	(- (* b_2 b_2) (* a c))
110.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
69.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.0s

Counts

308 → 308

Iterations

Iter	Nodes
2	2034
1	1003
0	360

prune3.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.4b

regimes342.0ms

Accuracy

82.6% (4.9b remaining)

Error of 10.4b against oracle of 5.5b and baseline of 33.9b

bsearch853.0ms

Steps

Iters	Range		Point
7	1.602087361235081e+82	9.448026055101687e+83	9.336288915836175e+83
8	-2.6682979144053964e-160	-2.716876171205868e-163	-2.640735663015172e-160
8	-4.1988061237604837e-88	-4.331385254994829e-91	-1.003636336181468e-90
9	-1.0131296714337304e-54	-1.526718807569313e-59	-1.0029215987945677e-54
7	-1.3734688567780161e-33	-7.936754581258996e-35	-1.6352743340081327e-34
7	-1.4003686841431728e+125	-2.978093086722774e+123	-3.035199252453359e+123

simplify22.0ms

Iterations

Iter	Nodes
2	47
1	47
0	44

end0.0ms

sample3.4s

Algorithm

intervals

Results

776.0ms	1035×	body	2560	valid
696.0ms	5859×	body	80	valid
569.0ms	958×	body	1280	valid
546.0ms	461×	body	640	valid
287.0ms	2918×	body	80	nan
135.0ms	106×	body	5120	valid
63.0ms	225×	body	320	valid
22.0ms	113×	body	160	valid